# Questions tagged [logic]

For questions about logic, whether it concerns syllogistic logic, mathematical logic or the nature of logic itself.

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51 views

### How to solve this natural deduction problem?

This one is driving me crazy. I don't understand most keys for de morgan, modus ponens, etc, so please abbreviate if possible? EX: DM, MP, SIMP, HS, Conj, Imp (material Implication). Thank you anybody ...
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### major/minor term of a syllogism when order of conclusion can be reversed

Consider: All ‘A’s are ‘B’s No ‘B’s are ‘C’s Is it not the case that the conclusion to this could either be: No ‘A’s are ‘C’s or No ‘C’s are ‘A’s ? Is it not also the case that the minor term ...
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### What if Euthyphro gave the opposite answer?

As part of a course I am taking, I was asked to continue the dialogue Euthyphro as if Euthyphro had given the opposite response to Plato's famous question: Is the pious loved by the gods because it ...
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### How to use use the Fitch System to prove (¬p ⇒ q) ⇒ ((¬p ⇒ ¬q) ⇒ p)?

I'm getting a bit stuck in a tailspin on this one. I'm quite new to logic. I'm not sure how or when we use negation to get P. How then does that connect to (¬p ⇒ q) ⇒ ((¬p ⇒ ¬q)?
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### Prerequisites for Michael Dummett texts

I want to read Michael Dummett's The Logical Basis of Metaphysics. Is it hard to read ? I would like an answer for the same question regarding his other texts. Do I need a prior exposition to other ...
87 views

### Which philosophers proposed theories containing a performative contradiction?

Socrates was blamed of this by being wrongly interpreted of saying: "I know that I don't Know." or other variants. What he really said was: "I neither know nor think that I know." Source: https://en....
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### What is the name of the fallacy where acknowledging an issue is confused with actually addressing the issue?

A few days ago an artist came to present his work to our class. At the beginning of his presentation he said "I know cultural appropriation is a very loaded topic, and it occupies my mind often" as ...
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### Are the “laws” of deductive logic empirically verifiable?

"Is Logic Empirical?" strongly suggests a question that I would like very much to get a handle on. That phrase is a title of an article by Hilary Putnam, and, according to synopses/reviews, the ...
224 views

### Language proof and logic Chapter 15 question 16 help

I'm trying to go about solving this problem but I'm having problems even knowing how to approach it. Can someone help me to set it up? Here is the premise: ∀x∀y(x ⊆ y ↔️ ∀z(z ∈ x ⟶ z ∈ y) Here is ...
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### I don't understand Parmenides's argument for why we can't think about what doesn't exist

I have been learning about Parmenides, and I don't think I am correctly understanding his argument for why we can't think/speak about things that don't exist. I tried to apply his logic to a ...
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### Given premise ~(P↔Q) how can one derive (~P↔Q) using Fitch?

Given premise ~(P↔Q) derive (~P↔Q) using Fitch-style natural deduction. I thought of simplifying the premise but I am still not able to find an answer. Can someone please help me?
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### Honestly have no Idea how to prove A v ¬¬B from A v B (LPL Q. 6.18)

Premise A v B Goal A v ¬¬B Please help. It seems so self evident but I don't know how to get there.
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### What logical fallacy considers a personal experience to be common place

While my wife and I were discussing the news a few days ago I stated that an argument expressed (in a news article, not by my wife) was a fallacy -- but I've been unable to put a name to it. ...
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### Why doesn't philosophy have higher standards for its arguments?

Mathematical systems are an excellent model for organizing and conducting thought: In the mathematics community, any argument in support of a conjecture, that deviates from "sound argument" never ...
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### What irreducible functions constitute thinking?

Because all new knowledge, to be not illogical, must obey logic i.e. every thinking step must be consistent with rules of logic; so can we write an effective procedure/algorithm which may be followed ...
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### Is it nonsense to say B -> [A -> B]?

Is it nonsense to say B → [A → B]? I would have thought so, it seems to say that every fact deductively follows from every other. But I was looking at a recent closed question, on natural deduction, ...
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### In First-Order Logic, can you deduce an existential quantifier purely from other existential quantifiers?

Let's say we have: ∃x(Fx → Gx) and ∃xFx can we deduce ∃xGx? I've been throwing myself at this problem for days and every time it just seems like the entire enterprise is flawed. Existential ...
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### How do you prove (p => q => r) => (p => q) => p => r using the Fitch system?

I'm quite new to logic. Thank you for taking the time to review this post. I tried the following and got to the conclusion I wanted but I was never able to prove the statement.
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### Cogito corollaries and meaning [closed]

Doubt implies thought. I'm doubting. So I'm thinking. [(d→t) ∧ d]→t Thought implies existence. I'm thinking. So I exist. [(t→e) ∧ t]→e d→t; ¬t→¬d; [¬t ∧ (d→t)]→¬d t→e; ¬e→¬t; [¬e ∧ (t→e)]→¬t [(d→...
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### Does the notion of an all-powerful God conflict with the idea of free will?

In Abrahamic religions, God is often believed to be wholly omnipotent. People also seem to believe that humans have "free will", especially insofar that they feel they are in control of their own ...
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### How is Wittgenstein’s “notorious paragraph” about the Gödel's Theorem not obviously correct?

Timm Lampert quotes from Wittgenstein's "notorious paragraph" (§8 of Remarks on the Foundations of Mathematics, Appendix 3) in http://wab.uib.no/agora/tools/alws/collection-6-issue-1-article-6....
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### Proof Universe Came From Nothing?

Consider the following proof: (1) Let the Universe be defined as the set of all things. (2) It is impossible for a thing to come from itself. (You can't be your own parent) (3) 2 implies a set of ...
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### Is the universe isomorphic to a universal turing machine?

I often think about problems that require an understanding of the very essence of computation and its inherent limitations. So, my questions are as followed: Is the universe isomorphic to a universal ...
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### Lists and predicates on lists in classical first order logic

I have to express some basic Prolog code in classical first order logic (FOL). In Prolog i use lists, together with member/2 and append/3 a lot. Could you give me some tips for writing clauses like ...
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### Concerning the definition of “valid”

I studying graduate math (not very far into it) and I realized that some of the higher level math texts I would like to read are hard to access without a strong basis in logic. Now I've taken ...
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Matter cannot be created. Cookies are matter. So cookies cannot be created. I know this seems absurd but I'm using this to make an important point about arguments. The argument appears to be valid ...
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### References for the Realism/Anti-Realism debate in Logic

The concept of anti-realism in logic seems to be an interesting and growing idea. I'm looking for references (papers, books, authors...) regarding the debate between realism and anti-realism but ...
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### Does the Universe make sense? [closed]

When faced with a paradox, we say: well this can't be because it doesn't make sense. p = "x doesn't make sense" q = "x doesn't exist" The contrapositive preserves validity: p implies q (not q) ...
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### Understanding the simulation argument

I came across Nick Bostrom's paper called Are You Living in a Computer Simulation?. The paper argues that at least one of the following propositions is true: The human species is likely to go extinct ...
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### Can someone explain this logical statement?

I have been trying to teach myself philosophical logic, but my mind is completely stuck. I cannot seem to understand the abstractions, which is unusual for me given that I have taken very advanced ...
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### The enunciation clause (Lyotard & Levinas)

As kind of introductory remark, let me state that I'm not academically-trained in philosophy, so my apologies if this comes up as a rather simple question. I was reading Logique de Levinas by JF ...
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### Why is there an O type conclusion in modus celaront

Modus celaront is type logical syllogism. No reptiles have fur. (MeP) All snakes are reptiles. (SaM) ∴ Some snakes have no fur. (SoP) The conclusion is of a O type(Some .. are not ...). Why is ...
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### Can there be cause and effect without time?

Our usual understanding of cause and effect operates tensely; that is in time. But consider a basic statement in some generic computer language: if x then y Is this in time? Well an actually ...
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### Trying to decide if the terms “proper education”, “real world education”, “successful life” are vague or ambiguous? [closed]

I feel that all three of these terms can have different meanings, but are they all vague as well? For example, proper education could mean a university education/college education/education in the ...
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If A, then B ~ A So, possible that B Valid or not? My take: Not valid. Reason: Valid means if all the premises are true, the conclusion must be true That means adding new information should not ...
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### What is the difference between logical consistency and logical entailment in deductive logic?

I am having a little trouble sorting out two definitions from the first chapter in my logic textbook, The Logic Book by Bergmann, Moor and Nelson. I am under the impression that a set in a sentence ...
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### Why do we need Aristotle's theory of predication?

My question is about Aristotle's theory of predication. Why do we need it at all? I know it's intuitive to pick up something and say something about it like "S is P", but doesn't this lead us to ...
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### When is pointing out a person's hypocrisy not considered to be a logical fallacy?

People keep using the word "whataboutism" and it seems people don't really know what it means, and I don't see how it's a logical fallacy if it's a very good argument. For instance, if the U.S. says ...
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### Incorrect statement in Suppes' Introduction to Logic

Chapter 2 of Suppes' develops the notion of sentential inference and how to construct rules of inference. However, there is one part in his development that seems incorrect no matter how I look at it. ...
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### Proof from tree to steps

I'm able to get the proof in a tree form (it's invalid). Is there a method where I can transform it to steps method indicating the rules of inference and replacement?
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### Negation of a relational quantified term?

Formally, when you negate a quantified term which is attached to a relation, is a distributed term always made undistributed and vice-versa? For example, consider this statement : Anyone who assists ...
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### What is the difference between a statement and a proposition?

I'm doing a MOOC on mathematical philosophy and the lecturer drew a distinction between a proposition and a statement. This is very puzzling to me. My background is in math and I regard those two ...
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### Has anyone developed a “restricted English” notation for logic (first-order or otherwise)?

I ask because Kleene mentions the possibility in Mathematical Logic, but I am not sure if he meant this as something he's aware of, or as a hypothetical possibility. I also enjoy the first part of ...
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### Logical Necessity

Logical necessity is that which is necessary by definition. Otherwise it is sometimes considered to be that which cannot possibly be false, or cannot be otherwise metaphysically. The usual example is ...
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### Who first studied asymmetric relations qua relation?

Who first asymmetric relations qua relation, viz., the fact that A relates to B by some relation does not always/necessarily imply that B relates to A by the same relation. ?
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### Using solipsism's incoherence with doubt as proof of the external world?

I have the following rough outline of utilizing solipsism as a proof by contradiction to the goal of asserting an epistemological proof of the external world. A solipsist (Wittgenstian) lives in a ...
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### Wittgenstein's solipsist, from Tractatus?

According to the early Wittgenstein of the Tractatus, the solipsist is one and one and the same with the world. He then makes the claim that solipsism coincides with realism. 5.64, Wittgenstein ...
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### De Morgan for Quantifiers Formal Proof: Inhabitance Question

I have a problem reading existing question's answers. I've successfully encoded the proof of one of De Morgan's Laws, ¬∃x P(x) → ∀x ¬P(x), for Quantifiers formally via cubicaltt type-checker via Curry-...